There’s a lot of different ways to find such quotes. One is to look up Commentaries on Genesis, sermons on Genesis, questions about Genesis, etc.
One is to look up verses in the Index Patrorum or Clavis Patrorum, or whatever it’s called, which is a partial index of Scripture quotes in the Fathers.
One is to have a subscription to one of the big Church Fathers services, and just search on the verse or phrase you want. If you are at a university, they may subscribe to stuff like that.
Similarly, you can search Google Books for the Latin, Greek, Hebrew, etc. for the phrase you want. For example, “lignum vitae” or other declensions of lignum, or “arbor vitae” and other declensions of arbor, and so on. If you want the Greek for a passage, either look it up on a Septuagint webpage, or go to Biblehub and click on the Greek for one of the Revelation passages, and then the Hebrew for one of the Genesis passages. (There are Syriac and Aramaic Bibles online, too.)
And there are also books that provide quotes and links, like the Ancient Christian Commentaries on Scripture series. (Intervarsity Press does that one, and it’s supposed to be more a bunch of good leads than a complete examination of everything the author says about a verse. More of a Protestant slant than a Catholic one.)
Bibles like the Navarre Bible have Fathers footnotes, too.
Anyway… you will want to look up references to all the Genesis verses mentioning the tree of life, as well as the Proverbs and Revelation verses.
